The equation for kinetic energy is,
Ke = (1/2)mv^2.
You're given a kinetic energy of 790 joules, and a speed of 1.6 m/s. Plugging these values into the equation, we get,
790 = (1/2)(1.6)^2(m).
Solving for m, we get,
m = (790)/(0.5(1.6)^2).
I'll let you crunch out those numbers for yourself :D
If you have any questions, feel free to ask. Hope this helps!
Answer:
15.106 N
Explanation:
From the given information,
The weight of the bucket can be calculated as:

The mass of the water accumulated in the bucket after 3.20s is:


To determine the weight of the water accumulated in the bucket, we have:



For the speed of the water before hitting the bucket; we have:


v = 8.4 m/s
Now, the force required to stop the water later when it already hit the bucket is:


F = 1.68 N
Finally, the reading scale is:
= 7.154 N + 6.272 N + 1.68 N
= 15.106 N
I would assume air resistance is negligible and so the acceleration of the package would be approximately 9.81 m/s².
Taking downwards as positive, use v²=u²+2as.
v²=(-2)²+2(9.81)(14)
v=16.7 m/s
Missing question in the text:
"A.What are the magnitude and direction of the electric field at the point in question?
B.<span>What would be the magnitude and direction of the force acting on a proton placed at this same point in the electric field?"</span>
<span>Solution:
A) A charge q </span>under an electric field of intensity E will experience a force F equal to:

In our problem we have
and
, so we can find the magnitude of the electric field:

The charge is negative, therefore it moves against the direction of the field lines. If the force is pushing down the charge, then the electric field lines go upward.
B) The proton charge is equal to

Therefore, the magnitude of the force acting on the proton will be

And since the proton has positive charge, the verse of the force is the same as the verse of the field, so upward.
Answer:
r = 4.44 m
Explanation:
For this exercise we use the Archimedes principle, which states that the buoyant force is equal to the weight of the dislodged fluid
B = ρ g V
Now let's use Newton's equilibrium relationship
B - W = 0
B = W
The weight of the system is the weight of the man and his accessories (W₁) plus the material weight of the ball (W)
σ = W / A
W = σ A
The area of a sphere is
A = 4π r²
W = W₁ + σ 4π r²
The volume of a sphere is
V = 4/3 π r³
Let's replace
ρ g 4/3 π r³ = W₁ + σ 4π r²
If we use the ideal gas equation
P V = n RT
P = ρ RT
ρ = P / RT
P / RT g 4/3 π r³ - σ 4 π r² = W₁
r² 4π (P/3RT r - σ) = W₁
Let's replace the values
r² 4π (1.01 10⁵ / (3 8.314 (70 + 273)) r - 0.060) = 13000
r² (11.81 r -0.060) = 13000 / 4pi
r² (11.81 r - 0.060) = 1034.51
As the independent term is very small we can despise it, to find the solution
r = 4.44 m